In that vein, can anybody put together a few links to help learn/understand the math behind the fourier series? Just from eyeballing I'd guess a solid understanding of integration of trigonometric functions, but I'm sure there's more to it.

The explanation is great. He shows the contribution of every single sin and cos and then shows some vibrations with a computer program which show all the harmonics which contribute to building the periodic function.

In that vein, can anybody put together a few links to help learn/understand the math behind the fourier series? Just from eyeballing I'd guess a solid understanding of integration of trigonometric functions, but I'm sure there's more to it.

Naele~

Fourier Series is a *special case* of a more general concept. Perhaps some key words you could look up online or in textbooks would be : orthogonality, basis states, fast fourier transform (FFT), orthonormal basis, maybe even Hilbert Space, or Gram Schmidt, or Legendre polynomials, or Sturm-Liouville.

(I know that Fourier series and the transform itself aren't the same thing, but I thought you might still like the videos)

I watched the whole 30 lecture series and they are very very good. I got so much out of it. Topics covered are Fourier Series, Fourier Transforms, convolutions, how they apply to linear systems in general, sampling, discrete Fourier Transforms, and higher dimensional Fourier Transforms. He also goes into good depth into how distributions like the Dirac Delta function are rigorously defined by Mathematicians. He's a great teacher and explains everything in such a way that it all seems natural. He's also quite funny too. You can download the whole course from iTunes U as well.